Math Word Problems Janet Hughes July 25, 2015 …jnhughes1225.weebly.com/uploads/2/5/3/8/25389299/tat_2...The Dick and Care five instructional component model based on Gagne’s nine

TAT 2 Task 3: Technology Production 1

TAT 2 Task 3: Integration Technology Production

Math Word Problems

Janet Hughes

July 25, 2015

Student ID: 000318949

Student Mentor: Carla Lee

A Written Project Presented to the Faculty of the Teachers College of

Western Governors University


Integration of Technology into the Instruction Unit: Math Word Problems

Instructor’s Manual

Table of Contents

Unit Overview

Instructional Goal

Audience

Length and Delivery Approach of Instructional Unit

Materials

Instructional and Lesson Overview

Lesson Plans for Unit of Instruction

Lesson 1:

Lesson 2:

Lesson 3:

Lesson 4:

Lesson 5:

Lesson 6:

Lesson 7:

Lesson 8:


Appendix


Unit Overview

Instructional Goal

Given a math word problem students will generate the correct equation to solve the problem on 8

out of 10 math word problems.

Audience

The fourth grade students of Buckeye South Elementary range in age from nine to eleven. On

the third grade Ohio Achievement Assessment (OAA) five of the students did not pass this

standardized test in math. Most of the students are proficient in basic math facts. During the

learner analysis, it was discovered that most students like math; in addition, most indicated they

sometimes know what to do with a math word problem.

In the fourth grade, four students have Individualized Educational Program (IEP) in

reading, two of these four have and IEP in math. They are proficient in basic math facts, but

have difficulties in reading math word problems and solving multi-step problems. They have

difficulties in remembering basic math algorithms.

The three periods of math are ability grouped based on their OAA scores. Instruction is

differentiated based on these ability groups. The lowest ability group in addition to verbal and

written instruction requires practice with math manipulatives. The middle and higher ability

groups are visual and auditory learners; occasionally they need math manipulatives for a more

hands on approach to learning.

The fourth grades students of Buckeye South Elementary, which is located in south

eastern Ohio in Jefferson County, are not a very ethnically diverse group of students. Out of 50

students two were biracial the rest are Caucasian. A large part of the student population was

from a low socio-economic background. The main industry in the town was a steel mill which


has been closed for a number of years. Several of the students come from single parent homes,

raised by a step parents, and a few were raised by grandparent/s. Southeastern Ohio is

considered Appalachia; therefore, due to topographical issues most of the students do not have

internet access. Socio-economics plays a part in this as well.

Length and Delivery Approach of Instructional Unit

This unit is designed to encompass ten days of instruction with eight different lessons.

One lesson will be taught of three days. Each lesson is one hour long. Each lesson will begin

with a review of prior knowledge from the third grade Common Core Standards and an

explanation of how prior knowledge is related to the new lesson. The instruction will begin with

a video from Pearson enVision Math website, practice problems from the text book or Moby

Max. When working with key words for math operations students will create collages to include

with graphic organizers in their interactive math notebooks. The teacher will formatively assess

students with observations and data from Moby Max. Data from Moby Max will be analyzed to

determine if any content needs reviewed for the whole class or just individual students. Lessons

that are based on basic math facts will have students working with the FlashMaster. The teacher

can formatively assess the students’ master of basic math facts by analyzing the time and number

correct students achieve on FlashMaster. At the end of the unit a summative assessment will be

given on the Pearson enVisionMath website. The teacher will select from a bank a problems the

number and types of problems to be assessed. The teacher will review the data from this

assessment to determine if the goals of the unit have been met.

Materials

Interactive white board

Teacher laptop


Student laptops

Student names on wooden sticks

Math binder with paper

Pencil

White boards, markers & erasers

Pearson enVisionMath textbook

Pearson enVisionMath website

Moby Max website

FlashMaster

Place value blocks

Math operations key word poster

Practice word problems

Construction paper

Markers or crayons

List of key words

Instructional and Lesson Overview

The design process used was Gagne’s nine events. Gagne’s nine events works well with

the Cognitive theory used, the instructor gains the attention of the students then informs them of

the lesson objective and then links to prior knowledge. Tapping into the prior knowledge

requires the students to access in their memory their knowledge of the subject. Then presenting

the instruction builds on their memory. Then by providing practice with guidance the instructor

helps embed this information in the students’ memory. Then placing the students into small

group helps the students further embed the information and receive feedback from peers and


instructor. The assessment will require the students to retrieve the information from their

memory and use their problem solving skills.

The learning theory that supports this instructional unit is Cognitivism. Math

requires the concept to be explained along with demonstration on how to solve is aligned with

the Cognitive Theory. The unit emphasizes practice with feedback from the instructor; practice

with corrective feedback helps embed the information. Cognitivism requires the learner to code

information, organize, rehearse, store, and then later retrieve the information. This unit of

instruction will require the students to code the key words into an organized list by operation in

their memory. The practice of word problems will require them to rehearse their knowledge and

help them store this information into long term memory for later retrieval. In the real world,

students will encounter math as a word problem not in an equation. For instance, calculating the

price of admission to an event for adults and children, problem solving is another math skill that

is appropriate for Cognitivism.

The Dick and Care five instructional component model based on Gagne’s nine events of

instruction was used. The Dick and Carey model takes Gagne’s nine events and combines them

into five instructional components. The preinstructional activities included gaining the attention

of the students and informing them of the lesson objective. Instruction of the new material

included demonstration on word problem solving skills by completing several examples. The

students them practiced their skills on word problems provided by the instructor with corrective

feedback. The assessment is a summative assessment that will analyze the students’ retrieval of

key words in math word problems. Follow-through activities include: review of instruction, the

collages, sharing of group math problems and practice of word problems.

Lesson Plans for Unit of Instruction


Lesson 1: Addition of 3 digits plus 3 digits and 4 digits plus 4 digits

Lesson Overview: This lesson is an extension of prior knowledge of 2 digits plus 2 digits

taught in 3rd grade. This lesson will demonstrate prior knowledge of regrouping of

numbers is carried over into adding multi-digit numbers.

Resources or Materials Needed:

Instructor

Interactive white board, laptop, enVisionMath website, student names on wooden

sticks

Students

Math binder with paper, pencil, white boards, markers, erasers, laptops,

enVisionMath website, FlashMaster

Lesson Objective: Given ten addition problems of 3 digits + 3 digits and 4 digits + 4 digits

problems the students will find the sum with 8 out of 10 accurately.

Time: Approximately 1 hour

Step 1 (Preinstructional Strategies): Link to prior knowledge of addition

The instructor will start the lesson by explaining the lesson objective to the students

Instructor will connect lesson to prior knowledge by demonstrating addition of 2 digit

plus 2 digit numbers with regrouping.

Instructor will write five problems on the interactive white board of 2 digit plus 2 digits

numbers and students will solve these problems in their math binder.


Five random students chosen from wooden sticks will solve these problems on interactive

white board. Others at desks will check their problems to those on board.

Step 2 (Content Presentation): Demonstration of addition of 3 digits + 3 digits and 4 digits + 4

digits with regrouping.

Instructor will show video on interactive whiteboard from enVisionMath website Topic

4.3

Instructor will demonstrate the addition of 3 digits + 3 digits and 4 digits + 4 digits with

regrouping on interactive white board.

Step 3 (Learner Participation): Practice problems

Students will be grouped in pairs and give each other addition problems of 3 digits + 3

digits and 4 digits + 4 digits with regrouping on white boards. The members of the pair

will check the others problems and explain errors if found.

Students demonstrating difficulties during pairing will work in a small group with the

instructor and use place value blocks to understand the concept of regrouping and

addition of 3 digits + 3 digits and 4 digits + 4 digits.

Students will practice basic addition math facts with FlashMaster

Teacher will monitor and provide feedback

Step 4 (Assessment): Practice Test

Instructor will write ten problems each of 3 digits + 3 digits and 4 digits + 4 digits with


Students will copy the problems in math binder and solve


Instructor will walk around room checking students’ work and providing feedback

Step 5 (Follow-through Activities):

Students will use laptops to complete activities on enVisionMath website on Topic 4.3

Instructor will review the lesson

Teacher will provide the students time to share problems from each of the pairs

As homework the students will write five problems of 3 digits + 3 digits and 4 digits + 4

digits with regrouping and solve.

Lesson 2: Addition Word Problems

Lesson Overview: This lesson will review the vocabulary of key words that indicate

addition, identify these key words in an addition word problem, form and equation and

solve.

Resources/Materials Needed:

Instructor:

Interactive white board, place value blocks, addition key words poster, copies of

written word problems, laptop, enVisionMath Website

Students:

Math binder with paper, pencil, white boards, marker, and erasers,

Lesson Objective(s):


Given a list of 10 key words the students will identify the words that indicate addition 8

out of 10 accurately.

Given a list of 10 key words the students will identify the words that indicate addition 8



Step 1 (Preinstructional Strategies):

Instructor will hang poster of key words that indicate addition on board

Students will write key words in math binder

Teacher will explain steps to solving word problems

Read the problem carefully 3 times

Underline the facts you will need to solve the problem

Circle the key word(s) that indicate the math operation

Write an equation

Solve the problem and show work

Check your answer

Students will write these steps in math binder

Step 2 (Content Presentation): Addition Word Problems

Instructor will show video on interactive whiteboard from enVisionMath website Topic

4.6

The instructor will model the steps to solving word problems using addition word

problems on the interactive white board.


Instructor will display an addition word problem on interactive white board and have

students read the problem three times.

The instructor will ask: “What are the facts you need to solve this problem?”

The instructor will ask: “What are the key word(s) that indicate addition?”

Instructor will write an equation based on the facts and key words identified by the

students

Instructor will solve, show work and check answer.

Instructor will work with whole group on several word problems with different addition

key words having students model the steps to solving addition word problems

Step 3 (Learner Participation): Solving Addition Word Problems

Students will work in pairs on addition word problems.

The pairs will read the problems 3 times

The members of each pair will take turns identifying the facts and key words in

each problem.

Each member will solve, show work, and check answers on white boards.


Step 4 (Assessment): Identifying Addition Key Words

Teacher will list on interactive white board key words for math operations

On white boards students will list the words that indicate addition

Students will hold up white boards when finished.

Teacher will provide feedback on their word


Step 4 (Follow-through Activity): Word Collage

Students will create a word collage of the key words for addition

Materials

Construction paper, markers, or crayons and list of addition key words

On construction paper

Write addition key words with markers or crayons using different fonts

Lesson 3: Subtraction of 3 digits – 3 digits, 4 digits – 4 digits problems

Lesson Overview: This lesson is an extension of prior knowledge of 2 digits minus 2 digits

taught in 3rd grade. This lesson will demonstrate prior knowledge of regrouping of

numbers is carried over into subtracting multi-digit numbers.

Resources/Materials Needed

Instructor

Interactive white board, student names on wooden sticks, laptop, enVisionMath

website

Students

Math binder with paper, pencil, white boards, markers, erasers, laptops, Moby

Max website, FlashMaster


Given ten subtraction problems of 3 digits – 3 digits and 4 digits – 4 digits the students will find

the difference 8 out of 10 accurately.



Step 1 (Preinstructional Strategies): Link to prior knowledge of subtraction


Instructor will connect lesson to prior knowledge by demonstrating subtraction of 2 digits

minus 2 digit numbers with regrouping.

Instructor will write five problems on the interactive white board of 2 digits minus 2

digits numbers and students will solve these problems in their math binder.



Step 2 (Content Presentation): Demonstration of subtraction of 3 digits - 3 digits and 4 digits -

4 digits with regrouping.

Instructor will so video from enVisionMath website on interactive whiteboard Topic 4.4

Instructor will demonstrate the subtraction of 3 digits - 3 digits and 4 digits - 4 digits with



Students will be grouped in pairs and give each other subtraction problems of 3 digits - 3

digits and 4 digits - 4 digits with regrouping on white boards. The members of the pair

will check the others problems and explain errors if found.


instructor and use place value blocks to understand the concept of regrouping and

addition of 3 digits - 3 digits and 4 digits - 4 digits.


Students will practice basic subtraction math facts on the FlashMaster



Students will complete assignment on laptop using the website Moby Max Adding and

Subtracting Whole Numbers





As homework the students will write five problems of 3 digits - 3 digits and 4 digits - 4

digits with regrouping and solve.

TITLE: Lesson 4: Subtraction Word Problems

Lesson Overview: This lesson will review the vocabulary of key words that indicate

subtraction, identify these key words in a subtraction word problem, form and equation

and solve.


Instructor:

Interactive white board, place value blocks, subtraction key words poster, copies

of written word problems

Students:


Math binder with paper, pencil, white boards, marker, and erasers


Given a list of 10 key words the students will identify the words that indicate subtraction

with 8 out of 10 accurately.

Given a list of 10 key words the students will identify the words that indicate subtraction

with 8 out of 10 accurately.



Instructor will hang poster of key words that indicate subtraction on board






Write an equation


Check your answer


Step 2 (Content Presentation): Subtraction Word Problems


The instructor will model the steps to solving word problems using subtraction word


Instructor will display a subtraction word problem on interactive white board and have



The instructor will ask: “What are the key word(s) that indicate subtraction?”


students


Instructor will work with whole group on several word problems with different

subtraction key words having students model the steps to solving subtraction word

problems

Step 3 (Learner Participation): Solving Subtraction Word Problems

Students will work in pairs on subtraction word problems.



each problem.



Step 4 (Assessment): Identifying Subtraction Key Words


On white boards students will list the words that indicate subtraction





Students will create a word collage of the key words for subtraction

Materials

Construction paper, markers, or crayons and list of subtraction key words


Write subtraction key words with markers or crayons using different fonts

TITLE: Lesson 5: Multiplication of 1 digit x 2 digits, 1 digit x 3 digits, 1 digit x 4 digits,

and 2 digits x 2 digits.

Lesson Overview: This lesson will explain the algorithms for multiplication of 1 digit x 2

digits, 1 digit x 3 digits, 1 digit x 4 digits, and 2 digits x 2 digits.


Instructor


website

Students

Math binder with paper, pencil, white boards, markers, erasers, laptops,

enVisionMath website, FlashMaster, Moby Max website

Lesson Objective(s:


Given ten multiplication problems of 1 digit x 2 digits the students will find the product with 8






Given ten multiplication problems of 2 digits x 2 digits the students will find the product with 8

out of 10 accurately

Time: Approximately 3 hours


The instructor will start the lesson by explaining the lesson objective to the

students

Instructor will review multiplication facts

Teacher will connect arrays to multiplication math sentences

Students will translate arrays to multiplication math sentences

Step 2 (Content Presentation): : Multiplication of 1 digit x 2 digits, 1 digit x 3 digits, 1 digit

x 4 digits, and 2 digits x 2 digits.

Instructor will use laptop to show on interactive whiteboard enVisionMath

website Topics 6.3, 6.4, & 8.4


Teacher will demonstrate on interactive white board how to multiply 1 digit x 2

digits, 1 digit x 3 digits, 1 digit x 4 digits, and 2 digits x 2 digits over the course of

the 3 hours of instruction.

Teacher will begin by demonstrating how to multiply 1 digit x 2 digits with

regrouping.

Then teacher will demonstrate how to multiply 1 digit x 3 digits and 1 digit x 4

digits with regrouping.

Instructor will connect the regrouping of multiplication to the regrouping of

addition.

Teacher will give students problems on the interactive white board that students

will copy to white boards and solve.

Students will hold boards up for teacher viewing and feedback.

Step 3 (Learner Participation): Practice Problems

Students will be grouped in pairs and give each other multiplication problems of 1 digit x

2 digits, 1 digit x 3 digits, 1 digit x 4 digits, and 2 digits x 2 digits with regrouping on

white boards. The members of the pair will check the other’s problems and explain

errors if found.

Students will use laptops to complete activites on enVisionMath website on Topics 6.3,

6.4 & 8.4


instructor to review multiplication algorithm.

Students will use FlashMaster to practice basic multiplication facts




Students will access the Moby Max website on the laptops and complete the assignment

on Multiplication.





As homework the students will write five problems of 1 digit x 2 digits, 1 digit x 3 digits,

1 digit x 4 digits, and 2 digits x 2 digits with regrouping and solve.

Lesson 6: Multiplication Word Problems

Lesson Overview: : This lesson will review the vocabulary of key words that indicate

multiplication, identify these key words in a multiplication word problem, form and

equation and solve.


Instructor



Students:


Math binder with paper, pencil, white boards, marker, erasers


Given a list of 10 key words the students will identify the words that indicate multiplication with

8 out of 10 accurately

Given ten multiplication word problems the students will identify the key words that indicate

multiplication, form an equation and solve 8 out of 10 accurately.



Instructor will hang poster of key words that indicate multiplication on board






Write an equation


Check your answer


Step 2 (Content Presentation): Multiplication Word Problems


The instructor will model the steps to solving word problems using multiplication word


Instructor will display a multiplication word problem on interactive white board and have



The instructor will ask: “What are the key word(s) that indicate multiplication?”


students


Instructor will work with whole group on several word problems with different

multiplication key words having students model the steps to solving multiplication word

problems

Step 3 (Learner Participation): Solving Multiplication Word Problems

Students will work in pairs on multiplication word problems.



each problem.



Step 4 (Assessment): Identifying Multiplication Key Words


On white boards students will list the words that indicate multiplication





Students will create a word collage of the key words for multiplication

Materials

Construction paper, markers, or crayons and list of multiplication key

words


Write multiplication key words with markers or crayons using different

fonts

Lesson 7: Division- 1 digit divisor with up to 3 digit dividend

Lesson Overview: This lesson is a study of inverse operations. Division is the inverse

operation of multiplication.


Instructor


website

Students

Math binder with paper, pencil, white boards, markers, erasers, graph paper,

laptops, FlashMaster, Moby Max website



Given ten division problems of 1 digit divisor with up to 3 digit dividend, no remainder students

will find the quotient 8 out of 10 accurately.


Step 1 (Preinstructional Strategies): Link to prior knowledge of division


Instructor will connect lesson to prior knowledge by demonstrating division as an inverse

operation of multiplication.

Instructor will write five problems each of the following on the interactive white board of

1 digit divisor with a 1 digit dividend, 1 digit divisor with a 2 digit dividend, 1 digit

divisor with a 3 digit dividend and students will solve these problems in their math binder

on graph paper.



Step 2 (Content Presentation): Demonstration of division of

Instructor will use laptop to show videos on the interactive whiteboard using

enVisionMath website Topics 10.4, 10.5, & 10.7

Instructor will demonstrate the division of 1 digit divisor with a 1 digit dividend, 1 digit

divisor with a 2 digit dividend, 1 digit divisor with a 3 digit dividend on interactive white

board.


Instructor will demonstrate on interactive white board with a background of graph paper

how students are to use graph paper to keep problem in proper alignment.


Students will use laptops to complete assignment on Moby Max website on Division

Students will be grouped in pairs and give each other division problems of 1 digit

dividend, 1 digit divisor with a 2 digit dividend, 1 digit divisor with a 3 digit dividend on

white boards. The members of the pair will check the others problems and explain errors

if found.


instructor reviewing the concept of inverse operations and the division algorithm



Instructor will write ten problems each of 1 digit dividend, 1 digit divisor with a 2 digit

dividend, 1 digit divisor with a 3 digit dividend on interactive white board.

Students will copy the problems in math binder and solve





As homework the students will write five problems 1 digit dividend, 1 digit divisor with a

2 digit dividend, and 1 digit divisor with a 3 digit dividend and solve.


Lesson 8: Division Word Problems

Lesson Overview: : This lesson will review the vocabulary of key words that indicate

division, identify these key words in a division word problem, form and equation and solve.


Instructor



Students:

Math binder with paper, pencil, white boards, marker, and erasers


Given a list of key words the students will identify the words that indicate division with 80%

accuracy

Given ten division word problems the students will identify the key words that indicate division,

form an equation and solve with 80% accuracy.



Instructor will hang poster of key words that indicate division on board







Write an equation


Check your answer


Step 2 (Content Presentation): Division Word Problems

The instructor will model the steps to solving word problems using division word


Instructor will display a division word problem on interactive white board and have



The instructor will ask: “What are the key word(s) that indicate division?”


students


Instructor will work with whole group on several word problems with different division

key words having students model the steps to solving division word problems

Step 3 (Learner Participation): Solving Division Word Problems

Students will work in pairs on division word problems.




each problem.



Step 4 (Assessment): Identifying Division Key Words


On white boards students will list the words that indicate division




Students will create a word collage of the key words for division

Materials

Construction paper, markers, or crayons and list of division key words


Write division key words with markers or crayons using different fonts


Appendix A

PDF Addition and Subtraction

Access online at https://www.mobymax.com/MM/SI/

School code: oh391

User name: wgu

Password: wgu

Math Tab

Appendix B

PDF Multiplication


School code: oh391

User name: wgu

Password: wgu

Math Tab

Appendix C

PDF Multiplication 2 Digit



School code: oh391

User name: wgu

Password: wgu

Math Tab

Appendix D

PDF Division


School code: oh391

User name: wgu

Password: wgu

Math Tab

Appendix E

PDF Summative Assessment

The summative assessment can be accessed online at www.pearsonsuccessnet.com

Log In

User name: Taskstream


Passowrd: Wgugrader1

To Do Tab

Summative Assessment

Appendix F

FlashMaster purchase at http://www.flashmaster.com/

Documents

Math Word Problems Janet Hughes July 25, 2015 …jnhughes1225.weebly.com/uploads/2/5/3/8/25389299/tat_2...The Dick and Care five instructional component model based on Gagne’s nine